Related papers: A Comparison of Limit Setting Methods for the On-O…
Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
We propose an analytical solution to the on-off problem within the framework of Bayesian statistics. Both the statistical significance for the discovery of new phenomena and credible intervals on model parameters are presented in a…
We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy…
Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…
Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…
We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
We introduce a general method, named the h-function method, to unify the constructions of level-alpha exact test and 1-alpha exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate…
We consider the problem of constructing confidence intervals for the median of a response $Y \in \mathbb{R}$ conditional on features $X \in \mathbb{R}^d$ in a situation where we are not willing to make any assumption whatsoever on the…
We propose an adaptive confidence interval procedure (CIP) for the coefficients in the normal linear regression model. This procedure has a frequentist coverage rate that is constant as a function of the model parameters, yet provides…
Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
A results of numerical procedure for construction of confidence intervals for parameter of Poisson distribution for signal in the presence of background which has Poisson distribution with known value of parameter are presented. It is shown…
We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…
Consider a linear regression model with n-dimensional response vector, regression parameter \beta = (\beta_1, ..., \beta_p) and independent and identically N(0, \sigma^2) distributed errors. Suppose that the parameter of interest is \theta…
Consider a two-treatment, two-period crossover trial, with responses that are continuous random variables. We find a large-sample frequentist 1-alpha confidence interval for the treatment difference that utilizes the uncertain prior…